## ELEMENTARY SYNTHETIC GEOMETRY OF THE POINT, LINE AND CIRCLE IN THE PLANE |

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Page vi

The properties of

distinguished. The principle of motion in the transformation of geometric figures,

as recommended by Dr. Sylvester, and as a consequence the principle of

continuity are freely ...

The properties of

**congruence**and equality are accordingly carefullydistinguished. The principle of motion in the transformation of geometric figures,

as recommended by Dr. Sylvester, and as a consequence the principle of

continuity are freely ...

Page 25

space and are said to be identically equal.

algebraic symbol of identity, = ; and this symbol placed between two figures

capable of ...

**Congruent**figures are distinguishable from one another only by their position inspace and are said to be identically equal.

**Congruence**is denoted by thealgebraic symbol of identity, = ; and this symbol placed between two figures

capable of ...

Page 26

Since two

— When two triangles have two sides and the included angle in the one

respectively equal to two sides and the included angle in the other, all the parts in

the ...

Since two

**congruent**triangles can be made to coincide in all their parts, therefore— When two triangles have two sides and the included angle in the one

respectively equal to two sides and the included angle in the other, all the parts in

the ...

Page 29

Hence a scalene triangle has no two angles equal to one another. 58°. Theorem.

–If two triangles have the three sides in the one respectively equal to the three

sides in the other the Proof.--Turn the AA'B'C' triangles are

...

Hence a scalene triangle has no two angles equal to one another. 58°. Theorem.

–If two triangles have the three sides in the one respectively equal to the three

sides in the other the Proof.--Turn the AA'B'C' triangles are

**Congruent**. B B' & C A'...

Page 30

3) and the triangles are

triangle is greater B than an internal opposite angle. The external angle BCD is

greater than the internal opposite angle ABC or c D BAC. A Proof.-Let BF be a ...

3) and the triangles are

**congruent**. q.e.d. 60°. Theorem.—An external angle of atriangle is greater B than an internal opposite angle. The external angle BCD is

greater than the internal opposite angle ABC or c D BAC. A Proof.-Let BF be a ...

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### Common terms and phrases

ABCD algebraic altitude base becomes called centre centre-line chord circle coincide collinear common concurrent congruent considered constant construct Converse corresponding cuts denote describe determine diagonals diameter difference direction distance divided draw drawn equal expressed external figure fixed point four geometric given given line given point gives greater harmonic Hence internal intersect inverse joins length lies line-segment mean measure median meet middle point opposite opposite sides orthogonally pair parallel passes pencil perpendicular perspective placed plane polar polygon position Proof proved quadrangle radical axis radius range ratio reciprocal rectangle regular relation remaining respect right angle right bisector rotation segment sides similar Similarly similitude square straight symbol taken tangent theorem touch triangle vertex vertices

### Popular passages

Page 176 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.

Page 183 - The sides of a triangle are proportional to the sines of the opposite angles.

Page 260 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...

Page 19 - Every circumference of a. circle, whether the circle be large or small, is supposed to be divided into 360 equal parts called degrees. Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.

Page 77 - J_ to the given line. .'. the construction gives the perpendicular to a given line at a given point in the line.

Page 122 - And conversely, if the square on one side of a triangle is equal to the Bum of the squares on the other two sides, the angle contained by these two sides is a right angle.

Page 124 - The difference of the squares of two sides of a triangle is equal to the difference of the squares of the segments made by the altitude upon the third side.